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Abstract

We generalize the recently proposed model for coherent beam combining in passive fiber laser arrays [Opt. Express 17, 19509 (2009)] to include the transient gain dynamics and the complication of counterpropagating waves, two important features characterizing actual experimental conditions. The extended model reveals that beam combining is not affected by the population relaxation process or the presence of backward propagating waves, which only serve to co-saturate the gain. The presence of nonresonant nonlinearity is found to reduce the coherent combining efficiency at high power levels. We show that the array lases at the frequencies with minimum overall losses when multiple loss mechanisms are present.

E. J. Bochove, “Effect of nonlinear phase on the passive phase locking of an array of fiber lasers of random lengths,” in Integrated Photonics and Nanophotonics Research and Applications (IPNRA) (Honolulu, Hawaii, 2009).

E. J. Bochove, “Effect of nonlinear phase on the passive phase locking of an array of fiber lasers of random lengths,” in Integrated Photonics and Nanophotonics Research and Applications (IPNRA) (Honolulu, Hawaii, 2009).

Figures (11)

The spatial distributions of one of the fiber laser (L1 = 24.3 m) are plotted as an example for (a) both propagating waves and (b) the gain field along the z axis. The three curves consisting of red circles present the self-consistent steady-state solutions obtained from our model, while that of solid black lines are calculated from Matlab with its built-in BVP solver. As for array dynamics, the time evolution of the output power and the averaged gain variable (over z) of each fiber are displayed in (c) and (d). The output power refers to the combined power coming out of the partially-reflected, R1, port as seen in Fig. 1.

Evolution diagram of the output power spectrum for (a) the array modes, (b) the zoom-in longitudinal modes and (c) the relative phase difference Δϕ (π) between two incident (backward) waves at z = 0. All of them start from random and noisy spontaneous emissions. The free spectral range in (b) is 4.1MHz.

An Er-doped fiber laser array in Fig. 1 with L1 24.3 and L2 24.0 m. The output powers from (a) upper port with partial reflectivity and (b) lower, angle-cleaved, port are plotted for time (left) and frequency (right) domains respectively. The separation between spikes in the frequency domain is 0.333 GHz.

A two-channel fiber laser array is simulated with γ = 0.9 W−1m−1. The array outputs are plotted in (a) and (b) respectively for both temporal (left) and spectral (right) domains. The relative phase difference of the circled spectral packets (in (a)) is plotted in (c) for nonlinear and in (d) for linear fiber laser arrays.

The frequency dependent losses (m−1), plotted in the log scale with blue lines, are overlapped with the lasing spectrum of the output fields (red spikes) for (a) zero and (b) nonzero b coefficients respectively.